Imaging Diffusion Processes

Diffusion Processes

cell may be seen (in a very simple model) as a compartmented space filled with liquid (cytoplasm) and containing numerous macro molecules (like proteins, RNA/DNA), single ions (sodium, chlorine...) and even bigger cellular organelles (like the cytoskeleton, mitochondria, the nucleus...). The function of the cell depends on chemical reactions of the molecules within it. As these reactions are often catalysed by proteins and are localized near dedicated cellular structures, the understanding of transport in the cell is essential. Many cellular reactions are diffusion controlled, i.e. the dominant transport process is diffusion. In addition there are also active transport mechanisms in the cell, like e.g. at membrane pores, or by kinesin which may drag particles along the cytoskeleton (see image below).

In many cases diffusion plays an important role. But these diffusive processes take place in a very complex environment, so we have to look at different types of diffusion:

  • If particles diffuse in a simple solution, like e.g. water, we observe normal Diffusion, which is governed by Fick’s law of diffusion. This implies that the mean squared displacement (MSD) σ2 of a particle increases linearly with time t:


This MSD describes the area that a particle may cover in a given time t. An example may be seen in the next image. It compares the trajectories of slow (red) to fast (magenta) particles, all for the same time span t. The circles symbolize the MSD for each of the particles within t. The faster the particle, the larger the MSD: The proportionality factor in the above relation between the MSD and the time is 6D, where D is the diffusion coefficient (measured in m2/s) which thus characterizes the speed of a particle. Typically this diffusion coefficient is in the range of 400μm2/s for small molecules in solution and 10-100μm2/s for intermediate sized proteins inside cells. The diffusion coefficient is a property that does not only depend on the particle, but also on its environment. This dependence is described by the Stokes-Einstein equation:

Here the diffusing particle is described by its hydrodynamic radius Rh, so the larger the the particle is, the slower it gets. The environment is characterized by its absolute temperature T (kB is Boltzma's constant) and its dynamic viscosity η.

  • Due to the crowding inside the cell the normal diffusive (brownian) motion may be hindered and results in so called sub-diffusion. Here crowding describes the fact that particles inside the cell do not move in a simple liquid, as above, but in a very complex environment. The cytosol is enriched with a multitude of different molecules and particles of very different sizes. Especially the larger partcles hinder the motion of the observed particles. The observed motion is then no longer normally diffusive, as above, but we observeanomalous subdiffusion. Here the MSD σ2 shows a time dependence, which is significantly slower than linear:

As one can see the spacial structure of the cell and the characteristics of the cellular environment significantly influence the motion of particles in the cell. Thus also the diffusion-dominated chemical reactions in the cells strongly depend on the local cellular environment. The other way round, the motion of these particles may be used to measure these environment properties. This explains why it is important to measure these motion properties in a spacially resolved manner in order to better understand the function of the whole cell.

Imaging Diffusion Processes

We use Fluorescence Correlation Spectroscopy (FCS), to generate a diffusion coefficient map with rather high accuracy and spacial resolution. A standard implementation of FCS is based on a confocal microscope and can thus only do a measurement on a single spot at a time. So in order to generate a complete map we have to do many single-spot measurements. We demonstrated the usability of this technique. The next image shows an example map of EGFP diffusing in a HeLa cell, created by single-spot FCS measurements (one measurement was done at each position marked with a white +):

This type of measurements leads to a long overall duration of the experiment and expose the cell to a lot of stress (laser illumination with rather high intensities) during this time. So we will now use a new technique, called Single Plane Illumination Microscopy Fluorescence Correlation Spectroscopy (SPIM-FCS) which allows us to do FCS measurements at different positions in the cell in parallel and also reduces the part of the cell that is illuminated to the actual measurement volume. In addition this technique allows us to also evaluate spacial data, which gives us acces to additional motion processes, like e.g. directed flow.

Details may be found in:

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